Code in Chapter 05: Practical Matters

\end{document}

print("Hats off to you, Prof. McFadden")
## [1] "Hats off to you, Prof. McFadden"
library(discrtr) # A companion package for the book Introduction to Discrete Choice Analysis with `R` 
library(dplyr) # A Grammar of Data Manipulation
library(ggplot2) # Create Elegant Data Visualisations Using the Grammar of Graphics
library(htmlwidgets) # HTML Widgets for R
library(kableExtra) # Construct Complex Table with 'kable' and Pipe Syntax 
library(mlogit) # Multinomial Logit Models 
library(plotly) # Create Interactive Web Graphics via 'plotly.js' 
library(stargazer) # Well-Formatted Regression and Summary Statistics Tables 
library(tidyr) # Tidy Messy Data
library(webshot2) # Take Screenshots of Web Pages
data("mc_commute_wide",
     package = "discrtr") 
example_wide <- mc_commute_wide %>%
  # Select columns from the table
  select(id, choice, starts_with("time")) %>%
  # Filter three decision-makers by their `id`
  # Here the symbol `|` is for "or", so this reads
  # filter rows with id == 566910139 OR id == 566873140 OR id == 566872636 
  filter(id == 566910139 |
           id == 566873140 |
           id == 566872636)

example_wide
##          id choice time.Cycle time.Walk time.HSR time.Car
## 1 566872636    HSR         NA  21.31439        5       NA
## 2 566873140    HSR         NA  12.78863       10        2
## 3 566910139   Walk   4.371118  15.00000       20        5
example_wide %>%
  # `pivot_longer()` takes a wide table and makes it long
  # Here we pivot the columns with the `time` variable 
  pivot_longer(cols = starts_with("time."),
               # There is a pattern to the names: time.ALTERNATIVE
               # The prefix is the name of the variable
               names_prefix = "time.",
               # The alternatives are placed in a new column called
               # "alternative"
               names_to = "alternative",
               # The values of the variables are consolidated in
               # a single column called "time"
               values_to = "time")
## # A tibble: 12 × 4
##           id choice alternative  time
##        <dbl> <fct>  <chr>       <dbl>
##  1 566872636 HSR    Cycle       NA   
##  2 566872636 HSR    Walk        21.3 
##  3 566872636 HSR    HSR          5   
##  4 566872636 HSR    Car         NA   
##  5 566873140 HSR    Cycle       NA   
##  6 566873140 HSR    Walk        12.8 
##  7 566873140 HSR    HSR         10   
##  8 566873140 HSR    Car          2   
##  9 566910139 Walk   Cycle        4.37
## 10 566910139 Walk   Walk        15   
## 11 566910139 Walk   HSR         20   
## 12 566910139 Walk   Car          5
example_long <- mc_commute_wide %>%
  # Filter three decision-makers by their `id`
  # Here the symbol `|` is for "or", so this reads
  # filter rows with id == 566910139 OR id == 566873140 OR id == 566872636 
  filter(id == 566910139 |
           id == 566873140 |
           id == 566872636) %>%
  mlogit.data(shape="wide", 
              # Name of column with the choices
              choice = "choice", 
              # Numbers of columns with attributes that vary by alternative
              varying = 3:22)

上面的结果导致Choice变成了True/False, 并且新增了一个alt (代表原来的”choice”)

data.frame(example_long) %>%
  # Select columns
  select(id, 
         choice, 
         alt, 
         starts_with("time"), 
         idx) 
##           id choice   alt      time    idx
## 1  566872636  FALSE   Car        NA  1:Car
## 2  566872636  FALSE Cycle        NA 1:ycle
## 3  566872636   TRUE   HSR  5.000000  1:HSR
## 4  566872636  FALSE  Walk 21.314387 1:Walk
## 5  566873140  FALSE   Car  2.000000  2:Car
## 6  566873140  FALSE Cycle        NA 2:ycle
## 7  566873140   TRUE   HSR 10.000000  2:HSR
## 8  566873140  FALSE  Walk 12.788632 2:Walk
## 9  566910139  FALSE   Car  5.000000  3:Car
## 10 566910139  FALSE Cycle  4.371118 3:ycle
## 11 566910139  FALSE   HSR 20.000000  3:HSR
## 12 566910139   TRUE  Walk 15.000000 3:Walk
print(data.frame(mc_commute_long$idx))
##      chid   alt
## 1       1   Car
## 2       1 Cycle
## 3       1   HSR
## 4       1  Walk
## 5       2   Car
## 6       2 Cycle
## 7       2   HSR
## 8       2  Walk
## 9       3   Car
## 10      3 Cycle
## 11      3   HSR
## 12      3  Walk
## 13      4   Car
## 14      4 Cycle
## 15      4   HSR
## 16      4  Walk
## 17      5   Car
## 18      5 Cycle
## 19      5   HSR
## 20      5  Walk
## 21      6   Car
## 22      6 Cycle
## 23      6   HSR
## 24      6  Walk
## 25      7   Car
## 26      7 Cycle
## 27      7   HSR
## 28      7  Walk
## 29      8   Car
## 30      8 Cycle
## 31      8   HSR
## 32      8  Walk
## 33      9   Car
## 34      9 Cycle
## 35      9   HSR
## 36      9  Walk
## 37     10   Car
## 38     10 Cycle
## 39     10   HSR
## 40     10  Walk
## 41     11   Car
## 42     11 Cycle
## 43     11   HSR
## 44     11  Walk
## 45     12   Car
## 46     12 Cycle
## 47     12   HSR
## 48     12  Walk
## 49     13   Car
## 50     13 Cycle
## 51     13   HSR
## 52     13  Walk
## 53     14   Car
## 54     14 Cycle
## 55     14   HSR
## 56     14  Walk
## 57     15   Car
## 58     15 Cycle
## 59     15   HSR
## 60     15  Walk
## 61     16   Car
## 62     16 Cycle
## 63     16   HSR
## 64     16  Walk
## 65     17   Car
## 66     17 Cycle
## 67     17   HSR
## 68     17  Walk
## 69     18   Car
## 70     18 Cycle
## 71     18   HSR
## 72     18  Walk
## 73     19   Car
## 74     19 Cycle
## 75     19   HSR
## 76     19  Walk
## 77     20   Car
## 78     20 Cycle
## 79     20   HSR
## 80     20  Walk
## 81     21   Car
## 82     21 Cycle
## 83     21   HSR
## 84     21  Walk
## 85     22   Car
## 86     22 Cycle
## 87     22   HSR
## 88     22  Walk
## 89     23   Car
## 90     23 Cycle
## 91     23   HSR
## 92     23  Walk
## 93     24   Car
## 94     24 Cycle
## 95     24   HSR
## 96     24  Walk
## 97     25   Car
## 98     25 Cycle
## 99     25   HSR
## 100    25  Walk
## 101    26   Car
## 102    26 Cycle
## 103    26   HSR
## 104    26  Walk
## 105    27   Car
## 106    27 Cycle
## 107    27   HSR
## 108    27  Walk
## 109    28   Car
## 110    28 Cycle
## 111    28   HSR
## 112    28  Walk
## 113    29   Car
## 114    29 Cycle
## 115    29   HSR
## 116    29  Walk
## 117    30   Car
## 118    30 Cycle
## 119    30   HSR
## 120    30  Walk
## 121    31   Car
## 122    31 Cycle
## 123    31   HSR
## 124    31  Walk
## 125    32   Car
## 126    32 Cycle
## 127    32   HSR
## 128    32  Walk
## 129    33   Car
## 130    33 Cycle
## 131    33   HSR
## 132    33  Walk
## 133    34   Car
## 134    34 Cycle
## 135    34   HSR
## 136    34  Walk
## 137    35   Car
## 138    35 Cycle
## 139    35   HSR
## 140    35  Walk
## 141    36   Car
## 142    36 Cycle
## 143    36   HSR
## 144    36  Walk
## 145    37   Car
## 146    37 Cycle
## 147    37   HSR
## 148    37  Walk
## 149    38   Car
## 150    38 Cycle
## 151    38   HSR
## 152    38  Walk
## 153    39   Car
## 154    39 Cycle
## 155    39   HSR
## 156    39  Walk
## 157    40   Car
## 158    40 Cycle
## 159    40   HSR
## 160    40  Walk
## 161    41   Car
## 162    41 Cycle
## 163    41   HSR
## 164    41  Walk
## 165    42   Car
## 166    42 Cycle
## 167    42   HSR
## 168    42  Walk
## 169    43   Car
## 170    43 Cycle
## 171    43   HSR
## 172    43  Walk
## 173    44   Car
## 174    44 Cycle
## 175    44   HSR
## 176    44  Walk
## 177    45   Car
## 178    45 Cycle
## 179    45   HSR
## 180    45  Walk
## 181    46   Car
## 182    46 Cycle
## 183    46   HSR
## 184    46  Walk
## 185    47   Car
## 186    47 Cycle
## 187    47   HSR
## 188    47  Walk
## 189    48   Car
## 190    48 Cycle
## 191    48   HSR
## 192    48  Walk
## 193    49   Car
## 194    49 Cycle
## 195    49   HSR
## 196    49  Walk
## 197    50   Car
## 198    50 Cycle
## 199    50   HSR
## 200    50  Walk
## 201    51   Car
## 202    51 Cycle
## 203    51   HSR
## 204    51  Walk
## 205    52   Car
## 206    52 Cycle
## 207    52   HSR
## 208    52  Walk
## 209    53   Car
## 210    53 Cycle
## 211    53   HSR
## 212    53  Walk
## 213    54   Car
## 214    54 Cycle
## 215    54   HSR
## 216    54  Walk
## 217    55   Car
## 218    55 Cycle
## 219    55   HSR
## 220    55  Walk
## 221    56   Car
## 222    56 Cycle
## 223    56   HSR
## 224    56  Walk
## 225    57   Car
## 226    57 Cycle
## 227    57   HSR
## 228    57  Walk
## 229    58   Car
## 230    58 Cycle
## 231    58   HSR
## 232    58  Walk
## 233    59   Car
## 234    59 Cycle
## 235    59   HSR
## 236    59  Walk
## 237    60   Car
## 238    60 Cycle
## 239    60   HSR
## 240    60  Walk
## 241    61   Car
## 242    61 Cycle
## 243    61   HSR
## 244    61  Walk
## 245    62   Car
## 246    62 Cycle
## 247    62   HSR
## 248    62  Walk
## 249    63   Car
## 250    63 Cycle
## 251    63   HSR
## 252    63  Walk
## 253    64   Car
## 254    64 Cycle
## 255    64   HSR
## 256    64  Walk
## 257    65   Car
## 258    65 Cycle
## 259    65   HSR
## 260    65  Walk
## 261    66   Car
## 262    66 Cycle
## 263    66   HSR
## 264    66  Walk
## 265    67   Car
## 266    67 Cycle
## 267    67   HSR
## 268    67  Walk
## 269    68   Car
## 270    68 Cycle
## 271    68   HSR
## 272    68  Walk
## 273    69   Car
## 274    69 Cycle
## 275    69   HSR
## 276    69  Walk
## 277    70   Car
## 278    70 Cycle
## 279    70   HSR
## 280    70  Walk
## 281    71   Car
## 282    71 Cycle
## 283    71   HSR
## 284    71  Walk
## 285    72   Car
## 286    72 Cycle
## 287    72   HSR
## 288    72  Walk
## 289    73   Car
## 290    73 Cycle
## 291    73   HSR
## 292    73  Walk
## 293    74   Car
## 294    74 Cycle
## 295    74   HSR
## 296    74  Walk
## 297    75   Car
## 298    75 Cycle
## 299    75   HSR
## 300    75  Walk
## 301    76   Car
## 302    76 Cycle
## 303    76   HSR
## 304    76  Walk
## 305    77   Car
## 306    77 Cycle
## 307    77   HSR
## 308    77  Walk
## 309    78   Car
## 310    78 Cycle
## 311    78   HSR
## 312    78  Walk
## 313    79   Car
## 314    79 Cycle
## 315    79   HSR
## 316    79  Walk
## 317    80   Car
## 318    80 Cycle
## 319    80   HSR
## 320    80  Walk
## 321    81   Car
## 322    81 Cycle
## 323    81   HSR
## 324    81  Walk
## 325    82   Car
## 326    82 Cycle
## 327    82   HSR
## 328    82  Walk
## 329    83   Car
## 330    83 Cycle
## 331    83   HSR
## 332    83  Walk
## 333    84   Car
## 334    84 Cycle
## 335    84   HSR
## 336    84  Walk
## 337    85   Car
## 338    85 Cycle
## 339    85   HSR
## 340    85  Walk
## 341    86   Car
## 342    86 Cycle
## 343    86   HSR
## 344    86  Walk
## 345    87   Car
## 346    87 Cycle
## 347    87   HSR
## 348    87  Walk
## 349    88   Car
## 350    88 Cycle
## 351    88   HSR
## 352    88  Walk
## 353    89   Car
## 354    89 Cycle
## 355    89   HSR
## 356    89  Walk
## 357    90   Car
## 358    90 Cycle
## 359    90   HSR
## 360    90  Walk
## 361    91   Car
## 362    91 Cycle
## 363    91   HSR
## 364    91  Walk
## 365    92   Car
## 366    92 Cycle
## 367    92   HSR
## 368    92  Walk
## 369    93   Car
## 370    93 Cycle
## 371    93   HSR
## 372    93  Walk
## 373    94   Car
## 374    94 Cycle
## 375    94   HSR
## 376    94  Walk
## 377    95   Car
## 378    95 Cycle
## 379    95   HSR
## 380    95  Walk
## 381    96   Car
## 382    96 Cycle
## 383    96   HSR
## 384    96  Walk
## 385    97   Car
## 386    97 Cycle
## 387    97   HSR
## 388    97  Walk
## 389    98   Car
## 390    98 Cycle
## 391    98   HSR
## 392    98  Walk
## 393    99   Car
## 394    99 Cycle
## 395    99   HSR
## 396    99  Walk
## 397   100   Car
## 398   100 Cycle
## 399   100   HSR
## 400   100  Walk
## 401   101   Car
## 402   101 Cycle
## 403   101   HSR
## 404   101  Walk
## 405   102   Car
## 406   102 Cycle
## 407   102   HSR
## 408   102  Walk
## 409   103   Car
## 410   103 Cycle
## 411   103   HSR
## 412   103  Walk
## 413   104   Car
## 414   104 Cycle
## 415   104   HSR
## 416   104  Walk
## 417   105   Car
## 418   105 Cycle
## 419   105   HSR
## 420   105  Walk
## 421   106   Car
## 422   106 Cycle
## 423   106   HSR
## 424   106  Walk
## 425   107   Car
## 426   107 Cycle
## 427   107   HSR
## 428   107  Walk
## 429   108   Car
## 430   108 Cycle
## 431   108   HSR
## 432   108  Walk
## 433   109   Car
## 434   109 Cycle
## 435   109   HSR
## 436   109  Walk
## 437   110   Car
## 438   110 Cycle
## 439   110   HSR
## 440   110  Walk
## 441   111   Car
## 442   111 Cycle
## 443   111   HSR
## 444   111  Walk
## 445   112   Car
## 446   112 Cycle
## 447   112   HSR
## 448   112  Walk
## 449   113   Car
## 450   113 Cycle
## 451   113   HSR
## 452   113  Walk
## 453   114   Car
## 454   114 Cycle
## 455   114   HSR
## 456   114  Walk
## 457   115   Car
## 458   115 Cycle
## 459   115   HSR
## 460   115  Walk
## 461   116   Car
## 462   116 Cycle
## 463   116   HSR
## 464   116  Walk
## 465   117   Car
## 466   117 Cycle
## 467   117   HSR
## 468   117  Walk
## 469   118   Car
## 470   118 Cycle
## 471   118   HSR
## 472   118  Walk
## 473   119   Car
## 474   119 Cycle
## 475   119   HSR
## 476   119  Walk
## 477   120   Car
## 478   120 Cycle
## 479   120   HSR
## 480   120  Walk
## 481   121   Car
## 482   121 Cycle
## 483   121   HSR
## 484   121  Walk
## 485   122   Car
## 486   122 Cycle
## 487   122   HSR
## 488   122  Walk
## 489   123   Car
## 490   123 Cycle
## 491   123   HSR
## 492   123  Walk
## 493   124   Car
## 494   124 Cycle
## 495   124   HSR
## 496   124  Walk
## 497   125   Car
## 498   125 Cycle
## 499   125   HSR
## 500   125  Walk
## 501   126   Car
## 502   126 Cycle
## 503   126   HSR
## 504   126  Walk
## 505   127   Car
## 506   127 Cycle
## 507   127   HSR
## 508   127  Walk
## 509   128   Car
## 510   128 Cycle
## 511   128   HSR
## 512   128  Walk
## 513   129   Car
## 514   129 Cycle
## 515   129   HSR
## 516   129  Walk
## 517   130   Car
## 518   130 Cycle
## 519   130   HSR
## 520   130  Walk
## 521   131   Car
## 522   131 Cycle
## 523   131   HSR
## 524   131  Walk
## 525   132   Car
## 526   132 Cycle
## 527   132   HSR
## 528   132  Walk
## 529   133   Car
## 530   133 Cycle
## 531   133   HSR
## 532   133  Walk
## 533   134   Car
## 534   134 Cycle
## 535   134   HSR
## 536   134  Walk
## 537   135   Car
## 538   135 Cycle
## 539   135   HSR
## 540   135  Walk
## 541   136   Car
## 542   136 Cycle
## 543   136   HSR
## 544   136  Walk
## 545   137   Car
## 546   137 Cycle
## 547   137   HSR
## 548   137  Walk
## 549   138   Car
## 550   138 Cycle
## 551   138   HSR
## 552   138  Walk
## 553   139   Car
## 554   139 Cycle
## 555   139   HSR
## 556   139  Walk
## 557   140   Car
## 558   140 Cycle
## 559   140   HSR
## 560   140  Walk
## 561   141   Car
## 562   141 Cycle
## 563   141   HSR
## 564   141  Walk
## 565   142   Car
## 566   142 Cycle
## 567   142   HSR
## 568   142  Walk
## 569   143   Car
## 570   143 Cycle
## 571   143   HSR
## 572   143  Walk
## 573   144   Car
## 574   144 Cycle
## 575   144   HSR
## 576   144  Walk
## 577   145   Car
## 578   145 Cycle
## 579   145   HSR
## 580   145  Walk
## 581   146   Car
## 582   146 Cycle
## 583   146   HSR
## 584   146  Walk
## 585   147   Car
## 586   147 Cycle
## 587   147   HSR
## 588   147  Walk
## 589   148   Car
## 590   148 Cycle
## 591   148   HSR
## 592   148  Walk
## 593   149   Car
## 594   149 Cycle
## 595   149   HSR
## 596   149  Walk
## 597   150   Car
## 598   150 Cycle
## 599   150   HSR
## 600   150  Walk
## 601   151   Car
## 602   151 Cycle
## 603   151   HSR
## 604   151  Walk
## 605   152   Car
## 606   152 Cycle
## 607   152   HSR
## 608   152  Walk
## 609   153   Car
## 610   153 Cycle
## 611   153   HSR
## 612   153  Walk
## 613   154   Car
## 614   154 Cycle
## 615   154   HSR
## 616   154  Walk
## 617   155   Car
## 618   155 Cycle
## 619   155   HSR
## 620   155  Walk
## 621   156   Car
## 622   156 Cycle
## 623   156   HSR
## 624   156  Walk
## 625   157   Car
## 626   157 Cycle
## 627   157   HSR
## 628   157  Walk
## 629   158   Car
## 630   158 Cycle
## 631   158   HSR
## 632   158  Walk
## 633   159   Car
## 634   159 Cycle
## 635   159   HSR
## 636   159  Walk
## 637   160   Car
## 638   160 Cycle
## 639   160   HSR
## 640   160  Walk
## 641   161   Car
## 642   161 Cycle
## 643   161   HSR
## 644   161  Walk
## 645   162   Car
## 646   162 Cycle
## 647   162   HSR
## 648   162  Walk
## 649   163   Car
## 650   163 Cycle
## 651   163   HSR
## 652   163  Walk
## 653   164   Car
## 654   164 Cycle
## 655   164   HSR
## 656   164  Walk
## 657   165   Car
## 658   165 Cycle
## 659   165   HSR
## 660   165  Walk
## 661   166   Car
## 662   166 Cycle
## 663   166   HSR
## 664   166  Walk
## 665   167   Car
## 666   167 Cycle
## 667   167   HSR
## 668   167  Walk
## 669   168   Car
## 670   168 Cycle
## 671   168   HSR
## 672   168  Walk
## 673   169   Car
## 674   169 Cycle
## 675   169   HSR
## 676   169  Walk
## 677   170   Car
## 678   170 Cycle
## 679   170   HSR
## 680   170  Walk
## 681   171   Car
## 682   171 Cycle
## 683   171   HSR
## 684   171  Walk
## 685   172   Car
## 686   172 Cycle
## 687   172   HSR
## 688   172  Walk
## 689   173   Car
## 690   173 Cycle
## 691   173   HSR
## 692   173  Walk
## 693   174   Car
## 694   174 Cycle
## 695   174   HSR
## 696   174  Walk
## 697   175   Car
## 698   175 Cycle
## 699   175   HSR
## 700   175  Walk
## 701   176   Car
## 702   176 Cycle
## 703   176   HSR
## 704   176  Walk
## 705   177   Car
## 706   177 Cycle
## 707   177   HSR
## 708   177  Walk
## 709   178   Car
## 710   178 Cycle
## 711   178   HSR
## 712   178  Walk
## 713   179   Car
## 714   179 Cycle
## 715   179   HSR
## 716   179  Walk
## 717   180   Car
## 718   180 Cycle
## 719   180   HSR
## 720   180  Walk
## 721   181   Car
## 722   181 Cycle
## 723   181   HSR
## 724   181  Walk
## 725   182   Car
## 726   182 Cycle
## 727   182   HSR
## 728   182  Walk
## 729   183   Car
## 730   183 Cycle
## 731   183   HSR
## 732   183  Walk
## 733   184   Car
## 734   184 Cycle
## 735   184   HSR
## 736   184  Walk
## 737   185   Car
## 738   185 Cycle
## 739   185   HSR
## 740   185  Walk
## 741   186   Car
## 742   186 Cycle
## 743   186   HSR
## 744   186  Walk
## 745   187   Car
## 746   187 Cycle
## 747   187   HSR
## 748   187  Walk
## 749   188   Car
## 750   188 Cycle
## 751   188   HSR
## 752   188  Walk
## 753   189   Car
## 754   189 Cycle
## 755   189   HSR
## 756   189  Walk
## 757   190   Car
## 758   190 Cycle
## 759   190   HSR
## 760   190  Walk
## 761   191   Car
## 762   191 Cycle
## 763   191   HSR
## 764   191  Walk
## 765   192   Car
## 766   192 Cycle
## 767   192   HSR
## 768   192  Walk
## 769   193   Car
## 770   193 Cycle
## 771   193   HSR
## 772   193  Walk
## 773   194   Car
## 774   194 Cycle
## 775   194   HSR
## 776   194  Walk
## 777   195   Car
## 778   195 Cycle
## 779   195   HSR
## 780   195  Walk
## 781   196   Car
## 782   196 Cycle
## 783   196   HSR
## 784   196  Walk
## 785   197   Car
## 786   197 Cycle
## 787   197   HSR
## 788   197  Walk
## 789   198   Car
## 790   198 Cycle
## 791   198   HSR
## 792   198  Walk
## 793   199   Car
## 794   199 Cycle
## 795   199   HSR
## 796   199  Walk
## 797   200   Car
## 798   200 Cycle
## 799   200   HSR
## 800   200  Walk
## 801   201   Car
## 802   201 Cycle
## 803   201   HSR
## 804   201  Walk
## 805   202   Car
## 806   202 Cycle
## 807   202   HSR
## 808   202  Walk
## 809   203   Car
## 810   203 Cycle
## 811   203   HSR
## 812   203  Walk
## 813   204   Car
## 814   204 Cycle
## 815   204   HSR
## 816   204  Walk
## 817   205   Car
## 818   205 Cycle
## 819   205   HSR
## 820   205  Walk
## 821   206   Car
## 822   206 Cycle
## 823   206   HSR
## 824   206  Walk
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## 5330 1333 Cycle
## 5331 1333   HSR
## 5332 1333  Walk
## 5333 1334   Car
## 5334 1334 Cycle
## 5335 1334   HSR
## 5336 1334  Walk
## 5337 1335   Car
## 5338 1335 Cycle
## 5339 1335   HSR
## 5340 1335  Walk
## 5341 1336   Car
## 5342 1336 Cycle
## 5343 1336   HSR
## 5344 1336  Walk
## 5345 1337   Car
## 5346 1337 Cycle
## 5347 1337   HSR
## 5348 1337  Walk
## 5349 1338   Car
## 5350 1338 Cycle
## 5351 1338   HSR
## 5352 1338  Walk
## 5353 1339   Car
## 5354 1339 Cycle
## 5355 1339   HSR
## 5356 1339  Walk
## 5357 1340   Car
## 5358 1340 Cycle
## 5359 1340   HSR
## 5360 1340  Walk
## 5361 1341   Car
## 5362 1341 Cycle
## 5363 1341   HSR
## 5364 1341  Walk
## 5365 1342   Car
## 5366 1342 Cycle
## 5367 1342   HSR
## 5368 1342  Walk
## 5369 1343   Car
## 5370 1343 Cycle
## 5371 1343   HSR
## 5372 1343  Walk
## 5373 1344   Car
## 5374 1344 Cycle
## 5375 1344   HSR
## 5376 1344  Walk
## 5377 1345   Car
## 5378 1345 Cycle
## 5379 1345   HSR
## 5380 1345  Walk
## 5381 1346   Car
## 5382 1346 Cycle
## 5383 1346   HSR
## 5384 1346  Walk
## 5385 1347   Car
## 5386 1347 Cycle
## 5387 1347   HSR
## 5388 1347  Walk
## 5389 1348   Car
## 5390 1348 Cycle
## 5391 1348   HSR
## 5392 1348  Walk
## 5393 1349   Car
## 5394 1349 Cycle
## 5395 1349   HSR
## 5396 1349  Walk
## 5397 1350   Car
## 5398 1350 Cycle
## 5399 1350   HSR
## 5400 1350  Walk
## 5401 1351   Car
## 5402 1351 Cycle
## 5403 1351   HSR
## 5404 1351  Walk
## 5405 1352   Car
## 5406 1352 Cycle
## 5407 1352   HSR
## 5408 1352  Walk
## 5409 1353   Car
## 5410 1353 Cycle
## 5411 1353   HSR
## 5412 1353  Walk
## 5413 1354   Car
## 5414 1354 Cycle
## 5415 1354   HSR
## 5416 1354  Walk
## 5417 1355   Car
## 5418 1355 Cycle
## 5419 1355   HSR
## 5420 1355  Walk
## 5421 1356   Car
## 5422 1356 Cycle
## 5423 1356   HSR
## 5424 1356  Walk
## 5425 1357   Car
## 5426 1357 Cycle
## 5427 1357   HSR
## 5428 1357  Walk
## 5429 1358   Car
## 5430 1358 Cycle
## 5431 1358   HSR
## 5432 1358  Walk
## 5433 1359   Car
## 5434 1359 Cycle
## 5435 1359   HSR
## 5436 1359  Walk
## 5437 1360   Car
## 5438 1360 Cycle
## 5439 1360   HSR
## 5440 1360  Walk
## 5441 1361   Car
## 5442 1361 Cycle
## 5443 1361   HSR
## 5444 1361  Walk
## 5445 1362   Car
## 5446 1362 Cycle
## 5447 1362   HSR
## 5448 1362  Walk
## 5449 1363   Car
## 5450 1363 Cycle
## 5451 1363   HSR
## 5452 1363  Walk
## 5453 1364   Car
## 5454 1364 Cycle
## 5455 1364   HSR
## 5456 1364  Walk
## 5457 1365   Car
## 5458 1365 Cycle
## 5459 1365   HSR
## 5460 1365  Walk
## 5461 1366   Car
## 5462 1366 Cycle
## 5463 1366   HSR
## 5464 1366  Walk
## 5465 1367   Car
## 5466 1367 Cycle
## 5467 1367   HSR
## 5468 1367  Walk
## 5469 1368   Car
## 5470 1368 Cycle
## 5471 1368   HSR
## 5472 1368  Walk
## 5473 1369   Car
## 5474 1369 Cycle
## 5475 1369   HSR
## 5476 1369  Walk
## 5477 1370   Car
## 5478 1370 Cycle
## 5479 1370   HSR
## 5480 1370  Walk
## 5481 1371   Car
## 5482 1371 Cycle
## 5483 1371   HSR
## 5484 1371  Walk
## 5485 1372   Car
## 5486 1372 Cycle
## 5487 1372   HSR
## 5488 1372  Walk
## 5489 1373   Car
## 5490 1373 Cycle
## 5491 1373   HSR
## 5492 1373  Walk
## 5493 1374   Car
## 5494 1374 Cycle
## 5495 1374   HSR
## 5496 1374  Walk
## 5497 1375   Car
## 5498 1375 Cycle
## 5499 1375   HSR
## 5500 1375  Walk
colnames(example_long)
##  [1] "id"                        "choice"                   
##  [3] "parking"                   "vehind"                   
##  [5] "gender"                    "age"                      
##  [7] "shared"                    "family"                   
##  [9] "child"                     "street_density"           
## [11] "sidewalk_density"          "LAT"                      
## [13] "LONG"                      "PersonalVehComf_SD"       
## [15] "PersonalVehComf_D"         "PersonalVehComf_A"        
## [17] "PersonalVehComf_SA"        "Fun_SD"                   
## [19] "Fun_D"                     "Fun_A"                    
## [21] "Fun_SA"                    "ActiveNeigh_SD"           
## [23] "ActiveNeigh_D"             "ActiveNeigh_A"            
## [25] "ActiveNeigh_SA"            "UsefulTrans_SD"           
## [27] "UsefulTrans_D"             "UsefulTrans_A"            
## [29] "UsefulTrans_SA"            "BusComf_SD"               
## [31] "BusComf_D"                 "BusComf_A"                
## [33] "BusComf_SA"                "TravelAlone_SD"           
## [35] "TravelAlone_D"             "TravelAlone_A"            
## [37] "TravelAlone_SA"            "Shelters_SD"              
## [39] "Shelters_D"                "Shelters_A"               
## [41] "Shelters_SA"               "Community_SD"             
## [43] "Community_D"               "Community_A"              
## [45] "Community_SA"              "personal_veh_comfortable" 
## [47] "getting_there_fun"         "like_active_neighborhood" 
## [49] "commute_useful_transition" "buses_comfortable"        
## [51] "prefer_travel_alone"       "shelter_good_quality"     
## [53] "sense_community"           "numna"                    
## [55] "alt"                       "available"                
## [57] "time"                      "access"                   
## [59] "wait"                      "transfer"                 
## [61] "chid"                      "idx"
?mc_commute_wide
# Function `mFormula()` is used to define multi-part formulas of the form:
# y ~ x | z | w, which in the notation used for the anatomy of utility functions is
# choice ~ alternative vars. with generic coefficients |
#          individual vars. with specific coefficients |
#          alternative vars. with specific coefficients 
# In this formula time is one of x variables
f1 <- mFormula(choice ~ time)
# Pipe `f1` to next function
f1 %>%
  # Build the model matrix with data set `example_long`
  model.matrix(example_long)
##   (Intercept):Cycle (Intercept):HSR (Intercept):Walk      time
## 1                 0               1                0  5.000000
## 2                 0               0                1 21.314387
## 3                 0               0                0  2.000000
## 4                 0               1                0 10.000000
## 5                 0               0                1 12.788632
## 6                 0               0                0  5.000000
## 7                 1               0                0  4.371118
## 8                 0               1                0 20.000000
## 9                 0               0                1 15.000000
# Function `mFormula()` is used to define multi-part formulas of the form:
# y ~ x | z | w, which in the notation used for the anatomy of utility functions is
# choice ~ alternative vars. with generic coefficients |
#          individual vars. with specific coefficients |
#          alternative vars. with specific coefficients 
# In this formula `time` is one of x variables and `sidewalk_density` is one of z variables
f2 <- mFormula(choice ~ time | sidewalk_density)
# Pipe `f2` to next function
f2 %>%
  # Build the model matrix with data set `example_long`
  model.matrix(example_long)
##   (Intercept):Cycle (Intercept):HSR (Intercept):Walk      time
## 1                 0               1                0  5.000000
## 2                 0               0                1 21.314387
## 3                 0               0                0  2.000000
## 4                 0               1                0 10.000000
## 5                 0               0                1 12.788632
## 6                 0               0                0  5.000000
## 7                 1               0                0  4.371118
## 8                 0               1                0 20.000000
## 9                 0               0                1 15.000000
##   sidewalk_density:Cycle sidewalk_density:HSR sidewalk_density:Walk
## 1                0.00000             22.63322               0.00000
## 2                0.00000              0.00000              22.63322
## 3                0.00000              0.00000               0.00000
## 4                0.00000             39.64003               0.00000
## 5                0.00000              0.00000              39.64003
## 6                0.00000              0.00000               0.00000
## 7               26.06793              0.00000               0.00000
## 8                0.00000             26.06793               0.00000
## 9                0.00000              0.00000              26.06793
f3 <- mFormula(choice ~ 0 | sidewalk_density | time)
# Pipe `f2` to next function
f3 %>%
  # Build the model matrix with data set `example_long`
  model.matrix(example_long)
##   (Intercept):Cycle (Intercept):HSR (Intercept):Walk sidewalk_density:Cycle
## 1                 0               1                0                0.00000
## 2                 0               0                1                0.00000
## 3                 0               0                0                0.00000
## 4                 0               1                0                0.00000
## 5                 0               0                1                0.00000
## 6                 0               0                0                0.00000
## 7                 1               0                0               26.06793
## 8                 0               1                0                0.00000
## 9                 0               0                1                0.00000
##   sidewalk_density:HSR sidewalk_density:Walk time:Car time:Cycle time:HSR
## 1             22.63322               0.00000        0   0.000000        5
## 2              0.00000              22.63322        0   0.000000        0
## 3              0.00000               0.00000        2   0.000000        0
## 4             39.64003               0.00000        0   0.000000       10
## 5              0.00000              39.64003        0   0.000000        0
## 6              0.00000               0.00000        5   0.000000        0
## 7              0.00000               0.00000        0   4.371118        0
## 8             26.06793               0.00000        0   0.000000       20
## 9              0.00000              26.06793        0   0.000000        0
##   time:Walk
## 1   0.00000
## 2  21.31439
## 3   0.00000
## 4   0.00000
## 5  12.78863
## 6   0.00000
## 7   0.00000
## 8   0.00000
## 9  15.00000
# Set the parameters:
mu <- 0
beta <- 0

# Calculate probabilities. Notice that these are the logit probabilities
# Individual 1
P1A <- (exp(beta * ts$xA[1])/
          (exp(beta * ts$xA[1]) + exp(mu + beta * ts$xB[1])))
P1B <- 1 - P1A
# Individual 2
P2A <- (exp(beta * ts$xA[2])/
          (exp(beta * ts$xA[2]) + exp(mu + beta * ts$xB[2])))
P2B <- 1 - P2A
# Individual 3
P3A <- (exp(beta * ts$xA[3])/
          (exp(beta * ts$xA[3]) + exp(mu + beta * ts$xB[3])))
P3B <- 1 - P3A
# Individual 4
P4A <- (exp(beta * ts$xA[4])/
          (exp(beta * ts$xA[4]) + exp(mu + beta * ts$xB[4])))
P4B <- 1 - P4A
# Individual 5
P5A <- (exp(beta * ts$xA[5])/
          (exp(beta * ts$xA[5]) + exp(mu + beta * ts$xB[5])))
P5B <- 1 - P5A
# Individual 6
P6A <- (exp(beta * ts$xA[6])/
          (exp(beta * ts$xA[6]) + exp(mu + beta * ts$xB[6])))
P6B <- 1 - P6A

# Calculate likelihood function as the product of all the probabilities
# Each probability is raised to ynj
L <-  P1A^ts$yA[1] * P1B^ts$yB[1] * 
  P2A^ts$yA[2] * P2B^ts$yB[2] * 
  P3A^ts$yA[3] * P3B^ts$yB[3] * 
  P4A^ts$yA[4] * P4B^ts$yB[4] * 
  P5A^ts$yA[5] * P5B^ts$yB[5] * 
  P6A^ts$yA[6] * P6B^ts$yB[6] 

# Create data frame to tabulate results:
df_experiment_1 <- data.frame(Individual = c(1, 2, 3, 4, 5, 6),
                              Choice = c("A", "A", "B", "A", "B", "B"),
                              PA = c(P1A, P2A, P3A, P4A, P5A, P6A),
                              PB = c(P1B, P2B, P3B, P4B, P5B, P6B))

# Display table
kable(df_experiment_1,
      "latex", 
      digits = 4, 
      booktabs = TRUE,
      align = c("l", "c", "c", "c")) %>%
  kable_styling(bootstrap_options = c("striped", "hover")) %>%
  footnote(general = paste("The value of the likelihood function in Example 1 is: ",
                           round(L, digits = 4)))
# Set the parameters:
mu <- 0.5
beta <- -0.5

# Calculate probabilities. Notice that these are the logit probabilities
# Individual 1
P1A <- (exp(beta * ts$xA[1])/
          (exp(beta * ts$xA[1]) + exp(mu + beta * ts$xB[1])))
P1B <- 1 - P1A
# Individual 2
P2A <- (exp(beta * ts$xA[2])/
          (exp(beta * ts$xA[2]) + exp(mu + beta * ts$xB[2])))
P2B <- 1 - P2A
# Individual 3
P3A <- (exp(beta * ts$xA[3])/
          (exp(beta * ts$xA[3]) + exp(mu + beta * ts$xB[3])))
P3B <- 1 - P3A
# Individual 4
P4A <- (exp(beta * ts$xA[4])/
          (exp(beta * ts$xA[4]) + exp(mu + beta * ts$xB[4])))
P4B <- 1 - P4A
# Individual 5
P5A <- (exp(beta * ts$xA[5])/
          (exp(beta * ts$xA[5]) + exp(mu + beta * ts$xB[5])))
P5B <- 1 - P5A
# Individual 6
P6A <- (exp(beta * ts$xA[6])/
          (exp(beta * ts$xA[6]) + exp(mu + beta * ts$xB[6])))
P6B <- 1 - P6A

# Calculate likelihood function as the product of all the probabilities
# Each probability is raised to ynj
L <-  P1A^ts$yA[1] * P1B^ts$yB[1] * 
  P2A^ts$yA[2] * P2B^ts$yB[2] * 
  P3A^ts$yA[3] * P3B^ts$yB[3] * 
  P4A^ts$yA[4] * P4B^ts$yB[4] * 
  P5A^ts$yA[5] * P5B^ts$yB[5] * 
  P6A^ts$yA[6] * P6B^ts$yB[6] 

# Create data frame to tabulate results:
df_experiment_2 <- data.frame(Individual = c(1, 2, 3, 4, 5, 6),
                              Choice = c("A", "A", "B", "A", "B", "B"),
                              PA = c(P1A, P2A, P3A, P4A, P5A, P6A),
                              PB = c(P1B, P2B, P3B, P4B, P5B, P6B))

# Display table
kable(df_experiment_2,
      "latex", 
      digits = 4, 
      booktabs = TRUE,
      align = c("l", "c", "c", "c")) %>%
  kable_styling(bootstrap_options = c("striped", "hover")) %>%
  footnote(general = paste("The value of the likelihood function in Example 2 is: ",
                           round(L, digits = 4)))
# Create a grid to plot the likelihood function
mu = seq(from = -1, to = 1, by = 0.05)
beta = seq(from = -2, to = 0, by = 0.05)
coeffs <- expand.grid(mu, beta)

# Define the likelihood function
lkh <- function(mu = 0, beta = 0){
  ts <- data.frame(Individual = c(1, 2, 3, 4, 5, 6),
                   Choice = c("A", "A", "B", "A", "B", "B"), 
                   yA = c(1, 1, 0, 1, 0, 0),
                   yB = c(0, 0, 1, 0, 1, 1),
                   xA = c(5, 2, 5, 1, 4, 3),
                   xB = c(4, 5, 2, 6, 1, 4))
  
  P1A <- (exp(beta * ts$xA[1])/
            (exp(beta * ts$xA[1]) + exp(mu + beta * ts$xB[1])))
  P1B <- 1 - P1A
  P2A <- (exp(beta * ts$xA[2])/
            (exp(beta * ts$xA[2]) + exp(mu + beta * ts$xB[2])))
  P2B <- 1 - P2A
  P3A <- (exp(beta * ts$xA[3])/
            (exp(beta * ts$xA[3]) + exp(mu + beta * ts$xB[3])))
  P3B <- 1 - P3A
  P4A <- (exp(beta * ts$xA[4])/
            (exp(beta * ts$xA[4]) + exp(mu + beta * ts$xB[4])))
  P4B <- 1 - P4A
  P5A <- (exp(beta * ts$xA[5])/
            (exp(beta * ts$xA[5]) + exp(mu + beta * ts$xB[5])))
  P5B <- 1 - P5A
  P6A <- (exp(beta * ts$xA[6])/
            (exp(beta * ts$xA[6]) + exp(mu + beta * ts$xB[6])))
  P6B <- 1 - P6A
  
  P1A^ts$yA[1] * P1B^ts$yB[1] * 
    P2A^ts$yA[2] * P2B^ts$yB[2] * 
    P3A^ts$yA[3] * P3B^ts$yB[3] * 
    P4A^ts$yA[4] * P4B^ts$yB[4] * 
    P5A^ts$yA[5] * P5B^ts$yB[5] * 
    P6A^ts$yA[6] * P6B^ts$yB[6] 
}

# Evaluate the likelihood function on the grid
L <- lkh(mu = coeffs$Var1, beta = coeffs$Var2)

L <- data.frame(mu = coeffs$Var1, beta = coeffs$Var2, L)
L <- xtabs(L ~ beta + mu, L) %>% # Convert to cross-tabulation matrix
  unclass() # Drop the xtabs class (plotly does not like it)

likelihood_plot <- plot_ly(z = ~L, x = ~mu, y = ~beta) %>% 
  add_surface() %>%
  layout(scene = list(
    xaxis = list(title = "x-axis (mu)"),
    yaxis = list(title = "y-axis (beta)"),
    zaxis = list(title = "$z$-axis (L)")))
# This code displays the figure in the Rmd document 
# but is not run for knitting to pdf
likelihood_plot
# Approximate values that maximize the likelihood function.
mu <- 0.10
beta <- -0.65

# Calculate probabilities. Notice that these are the logit probabilities
# Individual 1
P1A <- (exp(beta * ts$xA[1])/
          (exp(beta * ts$xA[1]) + exp(mu + beta * ts$xB[1])))
P1B <- 1 - P1A
# Individual 2
P2A <- (exp(beta * ts$xA[2])/
          (exp(beta * ts$xA[2]) + exp(mu + beta * ts$xB[2])))
P2B <- 1 - P2A
# Individual 3
P3A <- (exp(beta * ts$xA[3])/
          (exp(beta * ts$xA[3]) + exp(mu + beta * ts$xB[3])))
P3B <- 1 - P3A
# Individual 4
P4A <- (exp(beta * ts$xA[4])/
          (exp(beta * ts$xA[4]) + exp(mu + beta * ts$xB[4])))
P4B <- 1 - P4A
# Individual 5
P5A <- (exp(beta * ts$xA[5])/
          (exp(beta * ts$xA[5]) + exp(mu + beta * ts$xB[5])))
P5B <- 1 - P5A
# Individual 6
P6A <- (exp(beta * ts$xA[6])/
          (exp(beta * ts$xA[6]) + exp(mu + beta * ts$xB[6])))
P6B <- 1 - P6A

# Calculate likelihood function as the product of all the probabilities
# Each probability is raised to ynj
L <-  P1A^ts$yA[1] * P1B^ts$yB[1] * 
  P2A^ts$yA[2] * P2B^ts$yB[2] * 
  P3A^ts$yA[3] * P3B^ts$yB[3] * 
  P4A^ts$yA[4] * P4B^ts$yB[4] * 
  P5A^ts$yA[5] * P5B^ts$yB[5] * 
  P6A^ts$yA[6] * P6B^ts$yB[6] 

# Create data frame to tabulate results:
df_approx_solution <- data.frame(Individual = c(1, 2, 3, 4, 5, 6),
                                 Choice = c("A", "A", "B", "A", "B", "B"),
                                 PA = c(P1A, P2A, P3A, P4A, P5A, P6A),
                                 PB = c(P1B, P2B, P3B, P4B, P5B, P6B))

# Join tables for displaying results
df <- df_experiment_1 %>%
  left_join(df_experiment_2,
            by = c("Individual", "Choice")) %>%
  left_join(df_approx_solution,
            by = c("Individual", "Choice"))

# Display table
kable(df,
      "latex",
      digits = 4, 
      booktabs = TRUE,
      col.names = c("Individual", "Choice", "PA", "PB", "PA", "PB", "PA", "PB"),
      align = c("l", "c", "c", "c", "c", "c", "c", "c")) %>%
  kable_styling(latex_options = c("striped")) %>%
  add_header_above(c(" " = 1, " " = 1,
                     "Experiment 1" = 2, 
                     "Experiment 2" = 2, 
                     "Approx Max Likelihood" = 2))
mc_commute_long <- mc_commute_wide %>%
  mlogit.data(shape="wide", 
              # Name of column with the choices
              choice = "choice", 
              # Numbers of columns with attributes that vary by alternative
              varying = 3:22)
class(f1)
## [1] "mFormula" "Formula"  "formula"
class(f2)
## [1] "mFormula" "Formula"  "formula"
class(f3)
## [1] "mFormula" "Formula"  "formula"
# Function `mlogit()` is used to estimate logit models
# It needs a multi-part formula and a data set in long form
model1 <- mlogit(f1,
                 mc_commute_long)

# Function `summary()` give the summary of data objects,
# including the output of model estimation algorithms
summary(model1)
## 
## Call:
## mlogit(formula = choice ~ time, data = mc_commute_long, method = "nr")
## 
## Frequencies of alternatives:choice
##      Car    Cycle      HSR     Walk 
## 0.204364 0.034182 0.244364 0.517091 
## 
## nr method
## 5 iterations, 0h:0m:0s 
## g'(-H)^-1g = 0.000102 
## successive function values within tolerance limits 
## 
## Coefficients :
##                    Estimate Std. Error z-value  Pr(>|z|)    
## (Intercept):Cycle  0.366898   0.201434  1.8214   0.06854 .  
## (Intercept):HSR    0.707267   0.118104  5.9885 2.118e-09 ***
## (Intercept):Walk   3.212834   0.184169 17.4451 < 2.2e-16 ***
## time              -0.056494   0.005685 -9.9374 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Log-Likelihood: -768.63
## McFadden R^2:  0.50323 
## Likelihood ratio test : chisq = 1557.2 (p.value = < 2.22e-16)
# Note: use chunk option results="asis" to display latex output in pdf
stargazer::stargazer(model1, 
                     # Use type = "text", "latex". or "html" depending
                     # on the desired output
                     type ="latex",
                     header = FALSE,
                     single.row = TRUE,
                     title = "Estimation results: Model 1")
# Note: use chunk option results="asis" to display latex output in pdf
model2 <- mlogit(f2, 
                 mc_commute_long)

stargazer::stargazer(model2,
                     # Use type = "text", "latex". or "html" depending
                     # on the desired output
                     type = "latex",
                     header = FALSE,
                     single.row = TRUE,
                     title = "Estimation results: Model 2")
# Note: use chunk option results="asis" to display latex output in pdf
model2 <- mlogit(f2,
                 mc_commute_long, 
                 # Specify the alternative that acts as reference
                 reflevel = "Walk")

stargazer::stargazer(model2, 
                     # Use type = "text", "latex". or "html" depending
                     # on the desired output
                     type = "latex",
                     header = FALSE,
                     single.row = TRUE,
                     title = "Estimation results: Model 2 (alternative: Walk)")
summary(mc_commute_long$sidewalk_density)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    0.00   18.19   22.63   24.18   35.70   59.41
mc_commute_predict <- mc_commute_long[1:52,]
# Function `rep()` repeats the values in the argument a designated
# number of times; here, the values in the sequence 0 to 60 in intervals
# of 5 are repeated four times each (once for each alternative)
mc_commute_predict$sidewalk_density <- rep(seq(from = 0,
                                               to = 60,
                                               by = 5), 
                                           each = 4)
mc_commute_predict %>%
  data.frame() %>%
  select(sidewalk_density) %>%
  slice_head(n = 8)
##   sidewalk_density
## 1                0
## 2                0
## 3                0
## 4                0
## 5                5
## 6                5
## 7                5
## 8                5
median(mc_commute_predict$time, 
       na.rm = TRUE)
## [1] 10
mc_commute_predict$time <- 10
mc_commute_predict %>%
  data.frame() %>%
  select(time, sidewalk_density) %>%
  summary()
##       time    sidewalk_density
##  Min.   :10   Min.   : 0      
##  1st Qu.:10   1st Qu.:15      
##  Median :10   Median :30      
##  Mean   :10   Mean   :30      
##  3rd Qu.:10   3rd Qu.:45      
##  Max.   :10   Max.   :60
mc_commute_predict %>%
  data.frame() %>%
  select(time, sidewalk_density) %>%
  slice_head(n = 8)
##   time sidewalk_density
## 1   10                0
## 2   10                0
## 3   10                0
## 4   10                0
## 5   10                5
## 6   10                5
## 7   10                5
## 8   10                5
probs <- predict(model2, 
                 newdata = mc_commute_predict)
print(probs)
##         Walk        Car      Cycle        HSR
## 1  0.7381288 0.07072471 0.05208792 0.13905856
## 2  0.7646590 0.06149222 0.05191414 0.12193469
## 3  0.7887761 0.05323772 0.05152105 0.10646509
## 4  0.8105461 0.04591523 0.05093563 0.09260301
## 5  0.8300785 0.03946495 0.05018525 0.08027133
## 6  0.8475135 0.03381834 0.04929656 0.06937162
## 7  0.8630106 0.02890248 0.04829466 0.05979230
## 8  0.8767385 0.02464350 0.04720262 0.05141540
## 9  0.8888677 0.02096925 0.04604115 0.04412190
## 10 0.8995646 0.01781113 0.04482852 0.03779578
## 11 0.9089873 0.01510533 0.04358057 0.03232680
## 12 0.9172834 0.01279350 0.04231084 0.02761229
## 13 0.9245881 0.01082299 0.04103075 0.02355815
probs <- data.frame(sidewalk_density = seq(from = 0,
                                           to = 60, 
                                           by = 5), 
                    probs) %>% 
  # Pivot longer all columns _except_ `sidewalk_density`
  pivot_longer(cols = -sidewalk_density,
               # The column names become a new column called "Mode"
               names_to = "Mode",
               # The values are gathered into a single column called
               # "Probability"
               values_to = "Probability")
probs %>%
  slice_head(n = 8)
## # A tibble: 8 × 3
##   sidewalk_density Mode  Probability
##              <dbl> <chr>       <dbl>
## 1                0 Walk       0.738 
## 2                0 Car        0.0707
## 3                0 Cycle      0.0521
## 4                0 HSR        0.139 
## 5                5 Walk       0.765 
## 6                5 Car        0.0615
## 7                5 Cycle      0.0519
## 8                5 HSR        0.122
probs %>%
  # Create ggplot object; map `sidewalk_density` to the y-axis
  # `Probability` to the x-axis, and the color of geometric
  # objects to `Mode`
  ggplot(aes(x = sidewalk_density, 
             y = Probability,
             color = Mode)) +
  # Add geometric object of type line with size = 1
  geom_line(size = 1) +
  labs(y="Probability", 
       x = expression("Sidewalk density (km/km"^2*")")) 
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

f0 <- mFormula(choice ~ 1)

model0 <- mlogit(f0, 
                 mc_commute_long)

stargazer::stargazer(model0,
                     # Use type = "text", "latex". or "html" depending
                     # on the desired output
                     type = "latex",
                     header = FALSE,
                     single.row = TRUE,
                     title = "Estimation results: Market Shares Model (Null Model)")
1 - as.numeric(model2$logLik)/as.numeric(model0$logLik)
## [1] 0.5085353
lrtest(model1, 
       model2)
## Likelihood ratio test
## 
## Model 1: choice ~ time
## Model 2: choice ~ time | sidewalk_density
##   #Df  LogLik Df  Chisq Pr(>Chisq)    
## 1   4 -768.63                         
## 2   7 -760.42  3 16.429  0.0009258 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1